Import Question JSON

Current Question (ID: 19323)

Question:

$\text{A solid sphere and solid cylinder of identical radii approach an incline}$ $\text{with the same linear velocity (See figure). Both roll without slipping all}$ $\text{throughout. The two climb maximum heights } h_s \text{ and } h_c \text{ on the}$ $\text{incline. The ratio } \frac{h_s}{h_c} \text{ is given by:}$

Options:

1. $\frac{2}{\sqrt{5}}$
2. $\frac{14}{15}$
3. $\frac{4}{5}$
4. $1$

Solution:

$\text{Hint: Apply conservation of mechanical energy.}$ $\frac{1}{2}mv^2(1+\eta) = mgh$ $\frac{1}{h} \propto \frac{1}{1+\eta}$ $\frac{h_{sp}}{h_{cyl}} = \frac{1+\frac{2}{5}}{1+\frac{1}{2}} = \frac{7/5}{3/2} = \frac{14}{15}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}